I doubt its the IP address as few ISPs provide a static address. Most just dynamically allocate you an address from their batch every time you log on. If you have a broadband connection which is always on then try switching it off and then back on which might force the ISP to allocate you a new IP address. You don't say whether your computer is a laptop or not, but if it is try connecting wirelessly at a hotspot which will again mean using a completely different IP address. If you can sign up at the hotspot on your own PC its possible they are blocking your IP, but I doubt it.
My money is on a fairly craftily hidden cookie or piece of spyware on your computer which is identifying your computer to the website. Try running an anti-spyware device which may pick it up.
There is a remote chance they have identified the individual MAC addresses of the computers you use and are blockingthe machines themselves but that would probably be getting into conspiracy theory stuff and would more than likely be illegal!